Stereo matching Class 10 Read Chapter 7 Tsukuba dataset

Stereo Standard stereo geometry Stereo matching Correlation Optimization (DP, GC) General camera configuration Rectification Plane-sweep

Standard stereo geometry pure translation along X-axis

Standard stereo geometry

Stereo matching Search is limited to epipolar line (1D) Look for most similar pixel ?

Aggregation Use more than one pixel Assume neighbors have similar disparities * Use correlation window containing pixel Allows to use SSD, ZNCC, Census, etc.

Compare intensities pixel-by-pixel Comparing image regions I(x,y) I´(x,y) Sum of Square Differences Dissimilarity measures

Compare intensities pixel-by-pixel Comparing image regions I(x,y) I´(x,y) Zero-mean Normalized Cross Correlation Similarity measures

Compare intensities pixel-by-pixel Comparing image regions I(x,y) I´(x,y) Census Similarity measures (Real-time chip from TYZX based on Census) only compare bit signature

Aggregation window sizes Small windows disparities similar more ambiguities accurate when correct Large windows larger disp. variation more discriminant often more robust use shiftable windows to deal with discontinuities (Illustration from Pascal Fua)

Occlusions (Slide from Pascal Fua)

Real-time stereo on GPU Computes Sum-of-Square-Differences (use pixelshader) Hardware mip-map generation for aggregation over window Trade-off between small and large support window (Yang and Pollefeys, CVPR2003) 290M disparity hypothesis/sec (Radeon9800pro) e.g. 512x512x36disparities at 30Hz GPU is great for vision too!

Exploiting scene constraints

Ordering constraint , , , , surface slice surface as a path occlusion right occlusion left

Uniqueness constraint In an image pair each pixel has at most one corresponding pixel In general one corresponding pixel In case of occlusion there is none

Disparity constraint surface slice surface as a path bounding box disparity band use reconstructed features to determine bounding box constant disparity surfaces

Stereo matching Optimal path (dynamic programming ) Similarity measure (SSD or NCC) Constraints epipolar ordering uniqueness disparity limit Trade-off Matching cost (data) Discontinuities (prior) Consider all paths that satisfy the constraints pick best using dynamic programming

Hierarchical stereo matching Downsampling (Gaussian pyramid) Disparity propagation Allows faster computation Deals with large disparity ranges

Disparity map image I(x,y) image I´(x´,y´) Disparity map D(x,y) (x´,y´)=(x+D(x,y),y)

Example: reconstruct image from neighboring images

Energy minimization (Slide from Pascal Fua)

Graph Cut (Slide from Pascal Fua) (general formulation requires multi-way cut!)

(Boykov et al ICCV‘99) (Roy and Cox ICCV‘98) Simplified graph cut

Stereo matching with general camera configuration

Image pair rectification

Planar rectification Bring two views to standard stereo setup (moves epipole to  ) (not possible when in/close to image) ~ image size (calibrated) Distortion minimization (uncalibrated)

Polar re-parameterization around epipoles Requires only (oriented) epipolar geometry Preserve length of epipolar lines Choose  so that no pixels are compressed original image rectified image Polar rectification (Pollefeys et al. ICCV’99) Works for all relative motions Guarantees minimal image size

polar rectification planar rectification original image pair

Example: Béguinage of Leuven Does not work with standard Homography-based approaches

Example: Béguinage of Leuven

General iso-disparity surfaces ( Pollefeys and Sinha, ECCV’04) Example: polar rectification preserves disp. Application: Active vision Also interesting relation to human horopter

Stereo camera configurations (Slide from Pascal Fua)

Multi-camera configurations Okutami and Kanade (illustration from Pascal Fua)

Multi-view depth fusion Compute depth for every pixel of reference image Triangulation Use multiple views Up- and down sequence Use Kalman filter (Koch, Pollefeys and Van Gool. ECCV‘98) Allows to compute robust texture

Plane-sweep multi-view matching Simple algorithm for multiple cameras no rectification necessary doesn’t deal with occlusions Collins’96; Roy and Cox’98 (GC); Yang et al.’02/’03 (GPU)

Next class: structured light